This paper investigates several new hybrid cycles combining a solid/gas sorption refrigeration cycle with a Rankine cycle, and targeting three key functions: they are able to recover low-grade heat (for instance industrial waste heat), to store this energy, and to convert it into cold and/or power. Five operating modes have been designed, for either prevailing cold production or power generation. A thermodynamic analysis was performed to evaluate their energy and exergy performances, for a wide variety of reactive salts in the thermochemical system. Depending on the different modes and reactants, these hybrid thermochemical cycles can operate at temperatures as low as 87 °C. The share of power in total energy production lies between 0 and 30% for prevailing cold production modes, and between 50 and 100% for prevailing power generation modes. The energy and exergy efficiency reach 0.61 and 0.41, respectively. The energy storage density reaches about 170 kWh per m 3 of storage system. In some cases, additional power generation occurs during the charging step. Alternative systems performing the same functions and based on commercial systems have been designed and compared with hybrid thermochemical cycles. This comparison highlights that the energy storage density is lower for hybrid cycles. However, the global energy efficiency can be higher for hybrids, especially for prevailing cold production modes where it can be 34 % higher than for the alternative commercial system.